The number of permutations that can be made with the letters of the word "SRINATHDUBE", so that always a vowel occupies the central place is

SRINATHDUBE
Vowels $\to$ A, E, I, U $(4)$
Consonants $\to$ B, D, H, N, R, S, T $(7)$
$\to$ The central places can be occupied by $4$ different vowels. So, the no. of ways of allocating the central place $=4$
$\to$ The other $10$ places now have $10$ options left to choose from. So, the no. of ways to choose the remaining letters $=10!$
$\to$ So, the total no. of ways 
$=4\times 10!$